IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v173y2017i3d10.1007_s10957-017-1101-8.html
   My bibliography  Save this article

Formulas for Asymptotic Functions via Conjugates, Directional Derivatives and Subdifferentials

Author

Listed:
  • Felipe Lara

    (Universidad de Tarapacá)

  • Rubén López

    (Universidad de Tarapacá)

Abstract

The q-asymptotic function is a new tool that permits to study nonconvex optimization problems with unbounded data. It is particularly useful when dealing with quasiconvex functions. In this paper, we obtain formulas for the q-asymptotic function via c-conjugates, directional derivatives and subdifferentials. We obtain them under lower semicontinuity or local Lipschitz assumptions. The well-known formulas for the asymptotic function in the convex case are consequences of these ones. We obtain a new formula for the convex case.

Suggested Citation

  • Felipe Lara & Rubén López, 2017. "Formulas for Asymptotic Functions via Conjugates, Directional Derivatives and Subdifferentials," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 793-811, June.
    • Handle: RePEc:spr:joptap:v:173:y:2017:i:3:d:10.1007_s10957-017-1101-8
    DOI: 10.1007/s10957-017-1101-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-017-1101-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-017-1101-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. WEGGE, Leon L., 1974. "Mean value theorem for convex functions," LIDAM Reprints CORE 185, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Wegge, Leon L., 1974. "Mean value theorem for convex functions," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 207-208, August.
    3. Fabián Flores-Bazán & Fernando Flores-Bazán & Cristián Vera, 2015. "Maximizing and minimizing quasiconvex functions: related properties, existence and optimality conditions via radial epiderivatives," Journal of Global Optimization, Springer, vol. 63(1), pages 99-123, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alfredo Iusem & Felipe Lara, 2019. "Optimality Conditions for Vector Equilibrium Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 187-206, January.
    2. Felipe Lara, 2020. "Optimality Conditions for Nonconvex Nonsmooth Optimization via Global Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 134-150, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Eunji Lim, 2014. "On Convergence Rates of Convex Regression in Multiple Dimensions," INFORMS Journal on Computing, INFORMS, vol. 26(3), pages 616-628, August.
    2. J. P. Penot, 1997. "Mean-Value Theorem with Small Subdifferentials," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 209-221, July.
    3. Xu, Xingbai & Lee, Lung-fei, 2015. "Maximum likelihood estimation of a spatial autoregressive Tobit model," Journal of Econometrics, Elsevier, vol. 188(1), pages 264-280.
    4. Fabián Flores-Bazán & William Echegaray & Fernando Flores-Bazán & Eladio Ocaña, 2017. "Primal or dual strong-duality in nonconvex optimization and a class of quasiconvex problems having zero duality gap," Journal of Global Optimization, Springer, vol. 69(4), pages 823-845, December.
    5. A. Iusem & F. Lara, 2022. "Proximal Point Algorithms for Quasiconvex Pseudomonotone Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 443-461, June.
    6. Nicolas Hadjisavvas & Felipe Lara & Juan Enrique Martínez-Legaz, 2019. "A Quasiconvex Asymptotic Function with Applications in Optimization," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 170-186, January.
    7. F. Flores-Bazán & N. Hadjisavvas & F. Lara & I. Montenegro, 2016. "First- and Second-Order Asymptotic Analysis with Applications in Quasiconvex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 372-393, August.
    8. Nicolas Hadjisavvas & Felipe Lara & Dinh The Luc, 2020. "A general asymptotic function with applications in nonconvex optimization," Journal of Global Optimization, Springer, vol. 78(1), pages 49-68, September.
    9. Fabián Flores-Bazán & Filip Thiele, 2022. "On the Lower Semicontinuity of the Value Function and Existence of Solutions in Quasiconvex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 390-417, November.
    10. Felipe Lara, 2020. "Optimality Conditions for Nonconvex Nonsmooth Optimization via Global Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 134-150, April.
    11. Alfredo Iusem & Felipe Lara, 2019. "Optimality Conditions for Vector Equilibrium Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 187-206, January.
    12. Alfredo Iusem & Felipe Lara, 2019. "Existence Results for Noncoercive Mixed Variational Inequalities in Finite Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 122-138, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:173:y:2017:i:3:d:10.1007_s10957-017-1101-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.